# 2.03 Permeability.

The reluctance (S), of a material is a measure of how difficult it is to produce flux within it. Permeability, on the other hand, is a measure of how easily a magnetic field can be set up in a material. However, rather than just being a measure of the ratio of the m.m.f. to the flux it produces, permeability takes into account the distribution of the flux within the material. Permeability is the ratio of the flux density of the magnetic field within the material, to its field strength.

## u =B/H .

• u = the permeability of the material measured in Henries per metre (Hm-1).
• B = flux density measured in Tesla (T).
• H = the field strength measured in Amperes per metre (Am-1).

## Relative permeability

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When we refer to the permeability of a material, then rather than actually stating its absolute permeability, we tend to quote what is referred to, as its relative permeability. Relative permeability refers to how much more permeable the material is, in comparison to the absolute permeability of free space (i.e. a vacuum). The permeability of the material can be calculated by multiplying its relative permeability, by the permeability of free space.

## u = uo x ur .

• u = the permeability of the material measured in Henries per metre (Hm-1).
• uo = the permeability of free space measured in Henries per metre (Hm-1).
• ur = the relative permeability of the material (no units).

Note: the permeabilty of free space uo is 4 PI x10-7 H/m .
The relative permeability of air is very close to 1, so in practice we can use the same value for the permeability of air.

## Alternative description of permeability

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Another way we can think of permeability, is that it is a measure of how concentrated the magnetic flux is within the material, compared to how concentrated it would be in a vacuum.

## Relationship between reluctance and permeability

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At the beginning of this section we saw that the flux produced in a magnetic circuit, is proportional to the m.m.f and inversely proportional to the reluctance of the magnetic circuit. On this page, permeability has been described as a measure of how easy it is to set up a magnetic field within a material. The relationship between reluctance and permeability is:

## S=l/uA .

• S = reluctance.
• l = length of magnetic circuit.
• u = permeability of material.
• A = cross sectional area of magnetic circuit.

Therefore to produce a magnetic circuit with low reluctance, the circuit length should be kept short, the material chosen for the magnetic circuit should have a high permeability and the cross sectional area of the circuit should be large.